Lecture 1 - Introduction and History of Optimization
Lecture 2 - Basics of Linear Algebra
Lecture 3 - Definiteness of Matrices
Lecture 4 - Sets in R^n
Lecture 5 - Limit Superior and Limit Inferior
Lecture 6 - Order of Convergence
Lecture 7 - Lipschitz and Uniform Continuity
Lecture 8 - Partial and Directional Derivatives and Differnentiability (8,9)
Lecture 9 - Taylor's Theorem
Lecture 10 - Convex Sets and Convexity Preserving Operations
Lecture 11 - Sepration Results
Lecture 12 - Theorems of Alternatives (13 and 14)
Lecture 13 - Convex Functions
Lecture 14 - Properties and Zeroth Order Characterization of Convex Function
Lecture 15 - First-Order and Second-Order Characterization of Convex Functions
Lecture 16 - Convexity Preserving Operations
Lecture 17 - Optimality and Coerciveness
Lecture 18 - First-Order Optimality Condition (20 Part 1)
Lecture 19 - Second-Order Optimality Condition (20 Part 2)
Lecture 20 - General Structure of Unconstrained Optimization Algorithms
Lecture 21 - Inexact Line Search
Lecture 22 - Globel Convergence of Descent Methods (23,24)
Lecture 23 - Where Do Descent Methods Converge?
Lecture 24 - Scaling of Variables
Lecture 25 - Practical Stoping Criteria
Lecture 26 - Steepest Descent Method (28,29)
Lecture 27 - Newton's Method (30,31,32)
Lecture 28 - Quasi Newton Methods (33,34,35)
Lecture 29 - Conjugate Direction Methods (36,37)
Lecture 30 - Trust Region Methods - Part I
Lecture 31 - Trust Region Methods - Part II
Lecture 32 - A Revisit to Lagrange Multipliears Method
Lecture 33 - Special Cones for Contrained Optimization
Lecture 34 - Tangent Cone
Lecture 35 - First-Order KKT Optimality Conditions (42,43)
Lecture 36 - Second-Order KKT Optimality Conditions
Lecture 37 - Constraint Qualifications
Lecture 38 - Lagrangian Duality Theory (46 to 50)
Lecture 39 - Methods for Linearly Constrained Problems (51,52,53)
Lecture 40 - Interior-Point Method for QPP
Lecture 41 - Penalty Methods
Lecture 42 - Sequential Quadratic Programming Method
